Advice on Refinishing Ornate 1970s Bureau?

Q: My husband and I are both opera singers, so when someone gives us free stuff, we take it. This also means that we have some furniture that is…well… kinda ugly.

(Image credit: Cabiria)

(Image credit: Cabiria)

I would love to re-paint this old bedroom set (a bureau and two side tables), but I think I need to strip the current stain/varnish/coating/paint/whatever-the-heck-is-on-there first. However, there are SO MANY nooks and crannies, I don't know if it's even possible. Do they sell tiny electric sanders? Should I attach sand paper to a popsicle stick and just go at it? Help! I can't take it anymore!